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Uniqueness theorems for convex bodies in non‐Euclidean spaces
Author(s) -
Dulio Paolo,
Peri Carla
Publication year - 2002
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300016016
Subject(s) - mathematics , uniqueness , pure mathematics , convex set , manifold (fluid mechanics) , euclidean space , regular polygon , mathematical analysis , convex optimization , geometry , mechanical engineering , engineering
The notion of generalized X‐ray for star sets in a Riemannian manifold is introduced to prove uniqueness theorems for convex bodies contained in a simply convex neighbourhood of a two‐manifold. These results extend to the whole space and to arbitrary dimension when spaces of constant curvature are considered. As a consequence, a characterization of centrally symmetric convex bodies is obtained.